Rationale
Statements (1) and (2) TOGETHER are NOT sufficient.
The information provided in both statements does not allow us to determine whether the distance between Beth's home and Carol's home after they moved can be conclusively inferred. While statement (1) gives the total distance of the trip before the move, and statement (2) describes a percentage decrease in distance, neither statement provides enough detail about the actual distances involved or the specific changes after the move.
A) Statement (1) provides the total distance of 100 kilometers for the trip involving Ann, Beth, and Carol before any moves were made. While this indicates the overall travel distance, it does not supply information about the individual distances between the homes or the effects of the moves on those distances.
B) Statement (2) states that the distance between Beth's home and Carol's home decreased by 90% after they moved. However, this statement alone lacks context regarding the original distance between their homes, making it impossible to assess the new distance or its relevance to the overall scenario without further information.
C) Although both statements together provide some information about the distances involved, they do not collectively yield enough to determine the relationship between the distances after Beth and Carol moved. The original distances are unknown, and thus we cannot ascertain the implications of the 90% decrease.
D) Each statement alone fails to provide sufficient information regarding the distances between the homes, making it impossible to conclude anything definitive about the changes in distance due to the moves.
Conclusion
The analysis indicates that neither statement alone nor the two statements together furnish sufficient information to determine the new distance between Beth's and Carol's homes after their moves. The relationship between the distances remains ambiguous, confirming that further details would be necessary to arrive at a definitive conclusion regarding the situation.